Question: Simplify to lowest terms. $\dfrac{60}{100}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 60 and 100? $60 = 2\cdot2\cdot3\cdot5$ $100 = 2\cdot2\cdot5\cdot5$ $\mbox{GCD}(60, 100) = 2\cdot2\cdot5 = 20$ $\dfrac{60}{100} = \dfrac{3 \cdot 20}{ 5\cdot 20}$ $\hphantom{\dfrac{60}{100}} = \dfrac{3}{5} \cdot \dfrac{20}{20}$ $\hphantom{\dfrac{60}{100}} = \dfrac{3}{5} \cdot 1$ $\hphantom{\dfrac{60}{100}} = \dfrac{3}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{60}{100}= \dfrac{2\cdot30}{2\cdot50}= \dfrac{2\cdot 2\cdot15}{2\cdot 2\cdot25}= \dfrac{2\cdot 2\cdot 5\cdot3}{2\cdot 2\cdot 5\cdot5}= \dfrac{3}{5}$